Weyl function for sum of operators tensor products

The boundary triplets approach is applied to the construction of self-adjoint extensions of the operator having the form $S=A\otimes I_T+I_A\otimes T$ where the operator $A$ is symmetric and the operator $T$ is bounded and self-adjoint. The formula for the $\gamma$-field and the Weyl function corresponding the the boundary triplet $\Pi_S$ is obtained in terms of the $\gamma$-field and the Weyl function corresponding to the boundary triplet $\Pi_A$.